Talk:Meet and join: Difference between revisions

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::: Oh! Fascinating. Thanks for explaining your reasons here. I totally see your concern now. Personally, I haven't seen anyone use & to union commas/vectors like that, as in "81/80 & 64/63", but I agree my proposal would be clearly incompatible with that usage. The possibility hadn't occurred to me that Graham chose & for 5&7 = meantone not because it represented a meet of two temperaments, but rather because it represented a join of two maps, but I will ask him to clarify his thinking on that. Do you think this usage of & as a generic join/union operator is popular enough that you would dissuade others from using & for meeting temperaments and | for joining temperaments elsewhere? Or, to the best of your knowledge, is that just your personal practice? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:54, 19 December 2021 (UTC)

:::: Join has long been used in the sense where 7edo JOIN 12edo = meantone. So we should be consistent with this.

:::: Now some people like joining commas, such that 81/80 JOIN 128/125 = 12edo. This might be confusing because people use "augmented" for both 128/125 and the temperament defined by it.

:::: If we define join to only work on temperaments, there is no ambiguity:

:::: 7edo JOIN 12edo = meantone

:::: meantone MEET augmented = 12edo

:::: I have pursposefully avoided symbols above because they are irrelevant to that point.

:::: But I will suggest this: "join" has always been denoted with &, so it would be best to just use this symbol.

:::: So:

:::: 7edo & 12edo = meantone

:::: meantone | augmented = 12edo

:::: 81/80 | 128/125 = 12edo

:::: In my opinion this is the least ambiguous.

:::: Now for JI subspaces, I propose to define it such that:

:::: 2.3.7 & 2.3.5 = 2.3

:::: 2.3.7 | 2.3.5 = 2.3.5.7

:::: This neatly follows the meaning of the symbols when used as logical operators: with A | B takes all the elements in A or B. A & B takes only the elements in A and B. It also means that joining subspace temperaments joins both the subspace and the temperament, which seems nice.

:::: I am not in favor of introducing new symbols, especially since & has been in wide use specifically to denote the operation "join" on temperaments.

== Suggestion to add a helpful image ==

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 ::: Oh! Fascinating. Thanks for explaining your reasons here. I totally see your concern now. Personally, I haven't seen anyone use & to union commas/vectors like that, as in "81/80 & 64/63", but I agree my proposal would be clearly incompatible with that usage. The possibility hadn't occurred to me that Graham chose & for 5&7 = meantone not because it represented a meet of two temperaments, but rather because it represented a join of two maps, but I will ask him to clarify his thinking on that. Do you think this usage of & as a generic join/union operator is popular enough that you would dissuade others from using & for meeting temperaments and | for joining temperaments elsewhere? Or, to the best of your knowledge, is that just your personal practice? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:54, 19 December 2021 (UTC)
+:::: Join has long been used in the sense where 7edo JOIN 12edo = meantone. So we should be consistent with this.
+:::: Now some people like joining commas, such that 81/80 JOIN 128/125 = 12edo. This might be confusing because people use "augmented" for both 128/125 and the temperament defined by it.
+:::: If we define join to only work on temperaments, there is no ambiguity:
+:::: 7edo JOIN 12edo = meantone
+:::: meantone MEET augmented = 12edo
+:::: I have pursposefully avoided symbols above because they are irrelevant to that point.
+:::: But I will suggest this: "join" has always been denoted with &, so it would be best to just use this symbol.
+:::: So:
+:::: 7edo & 12edo = meantone
+:::: meantone | augmented = 12edo
+:::: 81/80 | 128/125 = 12edo
+:::: In my opinion this is the least ambiguous.
+:::: Now for JI subspaces, I propose to define it such that:
+:::: 2.3.7 & 2.3.5 = 2.3
+:::: 2.3.7 | 2.3.5 = 2.3.5.7
+:::: This neatly follows the meaning of the symbols when used as logical operators: with A | B takes all the elements in A or B. A & B takes only the elements in A and B. It also means that joining subspace temperaments joins both the subspace and the temperament, which seems nice.
+:::: I am not in favor of introducing new symbols, especially since & has been in wide use specifically to denote the operation "join" on temperaments.
 == Suggestion to add a helpful image ==